An emerging concept in cell signalling is the natural role of reactive oxygen species such as hydrogen peroxide (H2O2) as beneficial messengers in redox signalling pathways. The nature of H2O2 signalling is confounded, however, by difficulties in tracking it in living systems, both spatially and temporally, at low concentrations. Here, we develop an array of fluorescent single-walled carbon nanotubes that can selectively record, in real time, the discrete, stochastic quenching events that occur as H2O2 molecules are emitted from individual human epidermal carcinoma cells stimulated by epidermal growth factor. We show mathematically that such arrays can distinguish between molecules originating locally on the cell membrane from other contributions. We find that epidermal growth factor induces 2 nmol H2O2 locally over a period of 50 min. This platform promises a new approach to understanding the signalling of reactive oxygen species at the cellular level.